This invention pertains to joint inversion of remote geophysical data to infer geological properties of the subsurface. Remote geophysical data are likely to include active seismic reflection data; electromagnetic data (either controlled source (“CSEM”) or magneto-telluric (“MT”); and/or gravity measurements; however, any type of data that can be used to remotely infer the properties of subsurface rocks in the region of interest may be included. When multiple data types (e.g. reflection seismic and electromagnetic data) are inverted simultaneously, it is known as a joint inversion. During inversion the aim is to minimize the difference between the measured data and the data predicted by the inversion model. By combining multiple different types of geophysical data in a joint inversion, one often aims to invert for a model with multiple different types of model parameters (e.g. porosity and fluid type) rather than just a single parameter (e.g. p-wave impedance).
Due to the large number of model parameters and the often large computational cost of the forward calculation (“synthesizing” the data from a test model), one is often limited to linearized, local optimization techniques for inversion. These involve starting at an initial model and updating it by moving along a path in model-parameter space that decreases the misfit between measured data and synthesized data (known as the objective function). Geophysical inversion in general, and joint inversion in particular, often has a highly non-linear objective function which can result in poor convergence properties due to the solution becoming stuck in a local minimum of the objective function.
Lack of convergence due to strong non-linearity of the inversion problem often arises in geophysical inversion due to the nature of the seismic reflection data—specifically, the relative lack of low-frequency content in the data. This problem can be mitigated to some degree by first inverting a low-pass filtered version of the data to find a long-spatial-wavelength model. Using this model as a starting model for subsequent inversions of higher-frequency data can serve to stabilize the inversion process. The technique of first inverting low-frequency portion of the seismic reflection data can be combined with inverting only the earliest portions of the recorded data first, i.e. the earliest arrivals at the detectors. By limiting the time window during the inversion, the more complicated deeper reflections, which are overprinted by multiples, can be excluded to obtain a good shallow model.
Bunks et al. describe a multiscale approach to full waveform seismic inversion. (Bunks, C., Saleck, F. M., Zaleski, S., and Chavent, G., “Multiscale seismic waveform inversion,” Geophysics 50, 5, pp 1457-1473 (1995)) They propose to low-pass filter the seismic data and increase the model grid size in order to avoid many of the local minima normally encountered when inverting full waveform reflection seismic data. At each step, they add more frequencies to the data and reduce the grid size to realize the full resolution available in the data set. This method, however, does not describe how to stabilize a joint inversion of multiple data and parameter types.
Hu et al (2009) perform a joint inversion of electromagnetic and seismic data. (Hu, W., Abubakar, A., and Habashy, T. M., “Joint electromagnetic and seismic inversion using structural constraints,” Geophysics 74, 6, pp R99-R109 (2009)) In order to prevent high-frequency data from dominating the inversion and thus becoming trapped in local minima, they apply a weight to the data such that lower frequency portions of the data are emphasized. The data weighting does not change during the course of the inversion. This technique does not allow one to increase the influence of higher frequency data or to alter which parameters the inversion is solving for as the solution approaches the global minimum.